Download The University of Toledo TRIGONOMETRY PRACTICE TEST

The University of Toledo
TRIGONOMETRY PRACTICE TEST
This test consists of 20 questions. While you may take as much as you wish, it is
expected that you are able to complete it in about 45 minutes.
For proper course placement, please:
• Take the test seriously and honestly
• Do your own work without any assistance. Do not use any reference materials,
calculator, or any other computing aid
• Do not guess. If you don’t know how to work a problem, leave the answer blank.
1. The exact value of sin60 o is
3
3
2
B)
C)
A)
3
2
2
D)
1
2
E) none of the above
2. What is the radian measure of the angle whose degree measure are 300 o ?
4
11
11
5
π
A) π
B) π
C) π
D)
E) π
3
6
12
6
3
3
4
and cos θ =- ,then θ lies in
5
5
A) quadrant I
B) quadrant II
C) quadrant III D)quadrant IV E) none of the above
3. If sin θ = -
4. Of the following, which is the smallest?
π
π
π
A) sin0
B) sin
C) sin
D) sin(- )
6
4
3
E) sin
π
2
5. If the coordinates (x, y) of the point p in the figure are (2,2), then than sin(a)=
A) 1 3
2
3
5
C)
2
2
D)
2
E) 1
B)
6. The graph of the function y=-tan (x+ π /2) has asymptotes at
π
and x=2 π
2
π
3π
π
C) x= and x=
D) x= - and x= π
E) answer not given
2
2
2
7. Which of the following is the graph of y=sinx+4?
A) x=0 and x=
π
2
B) x=
(A)
(B)
(C)
(D)
(E)
8. The exact value of tan 60 o is
3π
1
1
D)
E)
3
2
2
3
4
π
π
9. The exact value of (cos 2 +tan ) is
4
4
1
1
3
A) 2
B) 1
C)
D)
E)
4
3
2
10. tanx cosx=
1
A) 1+tanx
B) sin x
C) – cosx
D)
E) none of the above
sin x
A)
3
B) 1
11. sin 2 30 o -tan45 o =
1
A) 1/4
B) 2
C)
C)
1
2
D) –3/4
E) none of the above
2
12. Perform the addition and simplify: 2 tan x cos x =
A) cos2x
B) 2sec 2 x +1 C) 2cos 2 x D) sin2x
E) none of the above
sin( x)
− cos x is equal to
tan( x)
A) tanx B) –sinx
C) cosx
13.
D) –cot x
E) 0
14. Which of the following is the graph of y=cos4x?
(A)
(B)
(C)
(D)
(E)
2
2
D) 0 o and 22.5 o
15. For which angles θ , with 0 o ≤ θ ≤ 180 o , is cos2 θ =
A) 22.5 o and 157.5 o
B) 60 o and 120 o
C) 125 o
16. If 2cos θ - 3 =0 and 0 o ≤ θ < 360 o , then
A) θ = 15 o or θ =165 o
B) θ = 60 o or θ = 120 o
C) θ = 30 o or θ = 150 o
D) θ = 30 o or θ = 330 o
E) none
E) θ = 30 o or θ = 210 o
17. For which values of x in the interval 0 < x < π does tan 2 x − tan x = 0 ?
π
π
π
3π
A) 0, and 2 π
B)
only
C) 0 and 1
D) 0, , and
E) none
2
4
2
2
18. In the figure shown, tan(a)+sina=
1
A) X (
+1)
X 2 +1
1+ X 2
X
1
C)
X
1
D)
+1
1+ X 2
X
E)
1+ X 2
B)
19. Evaluate cos −1 (
3
) . State your answer in radian measure. (Note: sin −1 means the
2
same as arcsin.)
π
π
B) A)
6
3
C) -
π
4
D) -
π
6
E)
π
4
20. Use an inverse trigonometric function to write a as a function of x.
4 − ( X + 1) 2
2
2
B) a =
X +1
C) a = 2 cos −1 ( X2 )
X +1
D) a = tan −1 (
)
2
4− X2
E) a = sin −1 (
)
2
A) a=
Solution:
1. B
2. E
3. C
4. D
5. D
6. E
7. D
8. A
9. E
10. E
11. D
12. D
13. E
14. C
15. A
16. D
17. E
18. A
19. A
20. E